Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


**Figure 13.**- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.


**Figure 13.**- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_pH 30 4.549826
mu_beta0_pH 5 4.339691
beta1_pH 31 2.356798
beta1_black 13 2.023708
beta0_black 6 1.936598
beta3_black 3 1.695922
beta2_yellow 3 1.653809
beta3_pH 23 1.580707
sd_comp 1 1.496897
beta2_pH 23 1.494580
beta0_yellow 2 1.417663
parameter n badRhat_avg
beta1_pelagic 6 1.374967
beta2_pelagic 8 1.332362
beta_H 1 1.325367
beta3_pelagic 3 1.311264
beta0_pelagic 5 1.291504
beta2_black 7 1.264959
tau_beta0_yellow 3 1.247653
tau_beta0_pH 4 1.226538
beta3_yellow 2 1.206006
tau_beta0_pelagic 2 1.205093
beta1_yellow 3 1.186122
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta_H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
beta0_black 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0
beta0_pelagic 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0 0
beta0_pH 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
beta0_yellow 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1
beta1_black 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0
beta1_pelagic 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1
beta1_pH 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
beta1_yellow 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1
beta2_black 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0
beta2_pelagic 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1
beta2_pH 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta2_yellow 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1
beta3_black 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0
beta3_pelagic 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1
beta3_pH 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1
beta3_yellow 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1
mu_beta0_pH 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.136 0.070 -0.272 -0.137 0.012
mu_bc_H[2] -0.094 0.046 -0.175 -0.099 0.009
mu_bc_H[3] -0.433 0.071 -0.571 -0.434 -0.293
mu_bc_H[4] -0.971 0.191 -1.356 -0.965 -0.595
mu_bc_H[5] 0.788 0.900 -0.223 0.620 2.955
mu_bc_H[6] -2.219 0.319 -2.848 -2.227 -1.579
mu_bc_H[7] -0.462 0.110 -0.682 -0.459 -0.261
mu_bc_H[8] 0.241 0.359 -0.357 0.205 1.051
mu_bc_H[9] -0.309 0.132 -0.566 -0.310 -0.050
mu_bc_H[10] -0.113 0.067 -0.237 -0.115 0.021
mu_bc_H[11] -0.103 0.040 -0.178 -0.104 -0.021
mu_bc_H[12] -0.242 0.104 -0.456 -0.240 -0.051
mu_bc_H[13] -0.127 0.078 -0.274 -0.126 0.029
mu_bc_H[14] -0.287 0.096 -0.476 -0.288 -0.103
mu_bc_H[15] -0.342 0.054 -0.442 -0.343 -0.228
mu_bc_H[16] -0.345 0.383 -1.027 -0.373 0.484
mu_bc_R[1] 1.370 0.147 1.085 1.370 1.661
mu_bc_R[2] 1.498 0.088 1.324 1.498 1.664
mu_bc_R[3] 1.439 0.135 1.175 1.441 1.698
mu_bc_R[4] 0.960 0.197 0.538 0.971 1.323
mu_bc_R[5] 1.214 0.435 0.350 1.227 2.036
mu_bc_R[6] -1.505 0.415 -2.359 -1.494 -0.704
mu_bc_R[7] 0.326 0.198 -0.072 0.332 0.711
mu_bc_R[8] 0.529 0.192 0.147 0.534 0.894
mu_bc_R[9] 0.367 0.196 -0.058 0.373 0.719
mu_bc_R[10] 1.295 0.136 1.028 1.298 1.550
mu_bc_R[11] 1.129 0.072 0.987 1.128 1.273
mu_bc_R[12] 0.942 0.192 0.564 0.940 1.332
mu_bc_R[13] 1.059 0.097 0.870 1.058 1.252
mu_bc_R[14] 0.982 0.146 0.702 0.979 1.271
mu_bc_R[15] 0.893 0.091 0.714 0.892 1.070
mu_bc_R[16] 1.216 0.124 0.977 1.213 1.459
tau_pH[1] 2.820 0.275 2.319 2.809 3.391
tau_pH[2] 2.937 0.397 2.251 2.906 3.786
tau_pH[3] 2.878 0.427 2.113 2.856 3.769
tau_pH[4] 9.402 2.240 5.572 9.207 14.384
tau_pH[5] 5.298 1.725 2.428 5.157 9.145
beta0_pH[1,1] 0.551 0.230 0.090 0.556 0.995
beta0_pH[2,1] 1.305 0.238 0.844 1.310 1.770
beta0_pH[3,1] 1.352 0.276 0.747 1.372 1.845
beta0_pH[4,1] 1.528 0.320 0.833 1.547 2.091
beta0_pH[5,1] -0.045 0.692 -1.152 -0.229 1.248
beta0_pH[6,1] 0.190 0.579 -0.986 0.311 1.058
beta0_pH[7,1] 0.394 0.574 -1.007 0.627 1.025
beta0_pH[8,1] -0.256 0.491 -1.124 -0.336 0.677
beta0_pH[9,1] -0.117 0.583 -1.093 -0.256 1.015
beta0_pH[10,1] 0.611 0.579 -0.421 0.487 1.691
beta0_pH[11,1] -0.341 0.288 -0.988 -0.322 0.176
beta0_pH[12,1] 0.465 0.283 -0.140 0.488 0.951
beta0_pH[13,1] 0.148 0.423 -0.493 0.081 1.088
beta0_pH[14,1] -0.403 0.267 -0.963 -0.397 0.098
beta0_pH[15,1] 0.092 0.607 -1.004 0.075 1.221
beta0_pH[16,1] 1.102 1.331 -1.148 1.872 2.556
beta0_pH[1,2] 2.502 0.215 2.100 2.496 2.914
beta0_pH[2,2] 2.776 0.238 2.245 2.802 3.172
beta0_pH[3,2] 2.419 0.237 1.937 2.434 2.837
beta0_pH[4,2] 2.395 0.288 1.800 2.398 2.918
beta0_pH[5,2] 1.829 3.209 -2.977 3.201 6.415
beta0_pH[6,2] 1.124 2.357 -2.804 2.598 3.250
beta0_pH[7,2] 0.435 2.082 -3.340 1.776 2.182
beta0_pH[8,2] 0.982 2.445 -2.899 2.620 3.064
beta0_pH[9,2] 0.876 2.558 -3.333 2.245 3.596
beta0_pH[10,2] 1.773 2.588 -2.270 3.466 3.968
beta0_pH[11,2] -4.879 0.284 -5.463 -4.875 -4.346
beta0_pH[12,2] -4.829 0.462 -5.843 -4.796 -4.015
beta0_pH[13,2] -4.690 0.377 -5.451 -4.688 -3.961
beta0_pH[14,2] -5.652 0.509 -6.668 -5.640 -4.722
beta0_pH[15,2] -4.164 0.329 -4.806 -4.154 -3.539
beta0_pH[16,2] -4.850 0.366 -5.575 -4.835 -4.143
beta0_pH[1,3] 1.359 0.247 0.838 1.369 1.796
beta0_pH[2,3] 1.818 0.406 0.974 1.889 2.419
beta0_pH[3,3] 1.960 0.469 1.064 1.968 2.675
beta0_pH[4,3] 2.174 0.644 1.021 2.223 3.113
beta0_pH[5,3] 0.995 1.802 -3.170 0.744 5.093
beta0_pH[6,3] -0.311 1.427 -2.350 -0.242 2.712
beta0_pH[7,3] -0.885 1.381 -3.329 -1.010 0.979
beta0_pH[8,3] 0.315 0.177 -0.023 0.316 0.658
beta0_pH[9,3] 0.088 0.342 -0.592 0.105 0.713
beta0_pH[10,3] 0.730 0.328 -0.048 0.757 1.277
beta0_pH[11,4] 0.560 1.113 -0.865 0.068 2.344
beta0_pH[12,4] 0.486 1.246 -1.306 -0.085 2.720
beta0_pH[13,4] 0.426 1.023 -0.845 -0.066 2.099
beta0_pH[14,4] 0.487 1.138 -1.011 -0.045 2.331
beta0_pH[15,4] 0.379 0.981 -0.659 -0.156 2.067
beta0_pH[16,4] 0.345 1.077 -0.665 -0.324 2.099
beta0_pH[11,5] -0.706 0.206 -1.133 -0.705 -0.299
beta0_pH[12,5] -2.455 0.362 -3.075 -2.471 -1.684
beta0_pH[13,5] -0.210 0.279 -0.768 -0.215 0.450
beta0_pH[14,5] -0.975 0.212 -1.383 -0.980 -0.556
beta0_pH[15,5] -1.132 0.181 -1.502 -1.131 -0.772
beta0_pH[16,5] -0.673 0.192 -1.043 -0.672 -0.283
beta1_pH[1,1] 3.130 0.418 2.360 3.100 4.012
beta1_pH[2,1] 2.479 0.440 1.730 2.435 3.495
beta1_pH[3,1] 2.651 0.601 1.800 2.545 4.124
beta1_pH[4,1] 3.323 0.791 2.272 3.149 5.216
beta1_pH[5,1] 1.681 0.703 0.461 1.736 3.006
beta1_pH[6,1] 2.486 1.061 1.099 2.239 4.993
beta1_pH[7,1] 1.718 0.924 0.391 1.552 4.032
beta1_pH[8,1] 3.032 1.221 1.338 2.892 6.338
beta1_pH[9,1] 1.782 0.648 0.609 1.868 3.038
beta1_pH[10,1] 1.991 0.870 0.706 2.040 4.105
beta1_pH[11,1] 6.729 0.889 5.331 6.577 8.747
beta1_pH[12,1] 2.922 0.335 2.314 2.897 3.624
beta1_pH[13,1] 5.591 1.082 3.883 5.407 8.125
beta1_pH[14,1] 14.970 3.959 9.512 14.183 24.925
beta1_pH[15,1] 8.191 1.886 5.116 7.923 12.005
beta1_pH[16,1] 12.038 2.903 6.929 12.067 18.669
beta1_pH[1,2] 1.232 1.953 0.075 0.958 4.510
beta1_pH[2,2] 3.225 8.178 0.088 0.942 28.490
beta1_pH[3,2] 1.199 0.287 0.661 1.192 1.803
beta1_pH[4,2] 1.507 3.253 0.063 0.777 11.598
beta1_pH[5,2] 6.947 18.437 0.000 2.740 31.692
beta1_pH[6,2] 2.541 2.090 0.000 1.665 5.955
beta1_pH[7,2] 2.475 3.501 0.000 1.180 7.830
beta1_pH[8,2] 2.313 2.374 0.000 1.017 5.881
beta1_pH[9,2] 2.736 2.445 0.000 1.566 6.777
beta1_pH[10,2] 4.294 4.445 0.000 3.675 18.547
beta1_pH[11,2] 6.798 0.326 6.183 6.791 7.461
beta1_pH[12,2] 6.760 0.632 5.722 6.701 8.184
beta1_pH[13,2] 7.186 0.421 6.386 7.179 8.056
beta1_pH[14,2] 7.556 0.538 6.598 7.554 8.654
beta1_pH[15,2] 6.705 0.355 6.034 6.695 7.413
beta1_pH[16,2] 7.580 0.393 6.831 7.568 8.359
beta1_pH[1,3] 1.888 0.451 1.116 1.872 2.721
beta1_pH[2,3] 0.934 0.917 0.001 0.780 3.715
beta1_pH[3,3] 3.531 7.726 0.005 0.961 30.994
beta1_pH[4,3] 1.195 1.619 0.001 1.021 3.667
beta1_pH[5,3] 4.351 3.732 1.376 3.310 13.979
beta1_pH[6,3] 3.597 2.946 0.768 2.921 11.343
beta1_pH[7,3] 2.392 1.467 0.248 2.388 5.026
beta1_pH[8,3] 2.702 0.328 2.075 2.705 3.341
beta1_pH[9,3] 1.993 0.393 1.239 1.989 2.756
beta1_pH[10,3] 2.653 0.413 1.942 2.624 3.557
beta1_pH[11,4] 2.258 1.369 0.135 2.606 4.894
beta1_pH[12,4] 2.404 1.256 0.227 2.956 4.251
beta1_pH[13,4] 2.089 1.317 0.119 2.424 5.057
beta1_pH[14,4] 1.895 1.049 0.088 2.322 3.438
beta1_pH[15,4] 1.829 0.990 0.097 2.278 3.104
beta1_pH[16,4] 1.955 0.930 0.223 2.465 2.964
beta1_pH[11,5] 11.667 11.418 1.270 7.308 45.849
beta1_pH[12,5] 21.098 44.379 3.504 10.781 94.399
beta1_pH[13,5] 13.728 11.880 2.847 10.247 43.032
beta1_pH[14,5] 11.162 8.407 1.918 8.368 30.982
beta1_pH[15,5] 15.863 19.616 2.292 9.022 74.552
beta1_pH[16,5] 19.411 31.154 2.690 10.991 138.386
beta2_pH[1,1] 0.485 0.241 0.256 0.453 0.877
beta2_pH[2,1] 0.520 0.518 0.183 0.414 1.469
beta2_pH[3,1] 0.454 0.442 0.156 0.374 1.205
beta2_pH[4,1] 0.346 0.170 0.139 0.318 0.721
beta2_pH[5,1] 1.725 3.093 -0.097 0.654 10.674
beta2_pH[6,1] 1.748 3.107 0.119 0.422 11.667
beta2_pH[7,1] -0.589 2.922 -8.605 0.028 3.928
beta2_pH[8,1] 1.140 2.239 0.142 0.385 8.275
beta2_pH[9,1] 1.489 2.667 0.175 0.543 9.739
beta2_pH[10,1] 1.649 2.520 0.137 0.681 9.715
beta2_pH[11,1] 0.233 0.052 0.147 0.229 0.346
beta2_pH[12,1] 1.111 0.599 0.425 0.964 2.649
beta2_pH[13,1] 0.267 0.071 0.162 0.256 0.437
beta2_pH[14,1] 0.246 0.038 0.184 0.243 0.330
beta2_pH[15,1] 0.208 0.055 0.132 0.198 0.343
beta2_pH[16,1] 0.513 0.427 0.129 0.472 1.476
beta2_pH[1,2] 2.461 5.114 -8.518 2.105 13.662
beta2_pH[2,2] -4.518 4.826 -17.402 -3.125 0.002
beta2_pH[3,2] -5.110 4.146 -16.079 -3.957 -0.664
beta2_pH[4,2] -4.546 4.035 -15.796 -3.475 -0.235
beta2_pH[5,2] 1.415 6.816 -12.410 1.977 15.402
beta2_pH[6,2] -0.735 7.092 -14.772 -1.743 13.196
beta2_pH[7,2] -0.716 6.708 -14.426 -1.278 12.465
beta2_pH[8,2] 0.379 6.939 -13.209 0.177 14.195
beta2_pH[9,2] -0.716 7.130 -14.751 -1.968 13.532
beta2_pH[10,2] -0.883 7.847 -15.491 -2.315 14.730
beta2_pH[11,2] -7.821 3.624 -17.400 -6.938 -3.382
beta2_pH[12,2] -2.712 2.577 -9.119 -1.598 -0.541
beta2_pH[13,2] -3.585 2.542 -10.760 -2.708 -1.326
beta2_pH[14,2] -4.909 2.856 -12.342 -4.043 -1.791
beta2_pH[15,2] -7.464 3.593 -17.391 -6.538 -3.433
beta2_pH[16,2] -7.789 3.466 -17.341 -6.935 -3.625
beta2_pH[1,3] 4.970 4.096 0.429 3.861 15.991
beta2_pH[2,3] 2.348 5.861 -10.809 2.182 14.806
beta2_pH[3,3] 0.292 6.470 -14.149 1.178 12.342
beta2_pH[4,3] 2.209 6.097 -11.879 2.353 14.503
beta2_pH[5,3] 5.331 4.369 -0.342 4.681 16.175
beta2_pH[6,3] 5.193 4.611 -2.941 4.648 15.680
beta2_pH[7,3] 3.048 5.772 -9.829 3.521 14.128
beta2_pH[8,3] 7.128 4.228 2.123 6.101 18.461
beta2_pH[9,3] 6.076 3.874 1.403 5.102 16.650
beta2_pH[10,3] 4.972 3.795 0.538 4.138 14.669
beta2_pH[11,4] -2.981 3.743 -13.808 -1.696 -0.002
beta2_pH[12,4] -3.515 3.924 -13.621 -2.234 1.632
beta2_pH[13,4] 1.436 4.618 -11.291 1.525 10.781
beta2_pH[14,4] -1.901 3.812 -12.495 -1.362 3.538
beta2_pH[15,4] 2.377 3.096 -1.286 1.711 10.878
beta2_pH[16,4] 5.189 4.109 0.441 4.534 14.708
beta2_pH[11,5] -2.887 2.129 -8.539 -2.307 -0.683
beta2_pH[12,5] -3.262 2.191 -8.960 -2.703 -0.783
beta2_pH[13,5] -3.285 2.331 -9.072 -2.711 -0.342
beta2_pH[14,5] -3.799 2.059 -8.492 -3.185 -1.165
beta2_pH[15,5] -3.880 2.196 -9.344 -3.211 -1.343
beta2_pH[16,5] -3.432 2.507 -9.707 -2.756 -0.705
beta3_pH[1,1] 35.901 1.098 33.890 35.827 38.274
beta3_pH[2,1] 34.368 1.946 31.368 34.032 39.223
beta3_pH[3,1] 35.765 2.026 32.395 35.543 40.630
beta3_pH[4,1] 36.329 2.127 32.984 36.060 41.235
beta3_pH[5,1] 31.195 4.618 21.359 30.614 42.686
beta3_pH[6,1] 40.742 2.837 34.018 41.661 45.165
beta3_pH[7,1] 32.513 10.121 18.827 31.772 45.831
beta3_pH[8,1] 39.920 2.049 35.894 39.828 44.754
beta3_pH[9,1] 32.695 3.347 28.055 32.021 41.512
beta3_pH[10,1] 33.864 1.927 30.967 33.587 38.210
beta3_pH[11,1] 35.433 1.429 33.032 35.306 38.456
beta3_pH[12,1] 30.375 0.588 29.115 30.408 31.452
beta3_pH[13,1] 39.193 1.985 35.546 39.073 43.441
beta3_pH[14,1] 41.571 1.822 38.451 41.444 45.424
beta3_pH[15,1] 41.149 2.799 36.013 41.182 45.722
beta3_pH[16,1] 44.628 0.886 42.739 44.702 45.922
beta3_pH[1,2] 38.082 6.789 19.647 40.599 44.564
beta3_pH[2,2] 33.222 6.066 21.107 32.929 44.630
beta3_pH[3,2] 41.910 1.124 40.095 41.916 44.138
beta3_pH[4,2] 38.691 6.880 21.001 41.416 45.409
beta3_pH[5,2] 30.527 6.962 18.947 28.088 44.963
beta3_pH[6,2] 31.651 5.681 20.079 34.033 41.703
beta3_pH[7,2] 28.066 6.833 19.030 24.939 44.468
beta3_pH[8,2] 29.347 6.277 18.576 28.981 43.594
beta3_pH[9,2] 36.467 8.489 21.750 41.930 45.675
beta3_pH[10,2] 30.574 5.183 20.547 29.485 41.937
beta3_pH[11,2] 43.349 0.154 43.106 43.333 43.700
beta3_pH[12,2] 43.119 0.257 42.494 43.138 43.583
beta3_pH[13,2] 43.835 0.136 43.540 43.853 44.057
beta3_pH[14,2] 43.325 0.164 43.078 43.310 43.682
beta3_pH[15,2] 43.388 0.161 43.121 43.373 43.739
beta3_pH[16,2] 43.491 0.166 43.184 43.488 43.816
beta3_pH[1,3] 40.062 0.807 38.461 40.103 41.383
beta3_pH[2,3] 32.027 6.626 19.103 32.797 44.882
beta3_pH[3,3] 31.574 7.211 18.788 31.993 43.948
beta3_pH[4,3] 27.521 6.814 18.332 26.623 44.580
beta3_pH[5,3] 27.002 6.226 18.376 26.211 42.852
beta3_pH[6,3] 31.131 5.820 19.153 31.871 44.326
beta3_pH[7,3] 26.108 4.828 18.786 25.044 41.546
beta3_pH[8,3] 41.496 0.227 41.072 41.504 41.911
beta3_pH[9,3] 33.798 0.527 33.002 33.802 34.815
beta3_pH[10,3] 36.015 0.575 34.495 36.081 36.879
beta3_pH[11,4] 40.147 5.004 29.485 42.959 45.811
beta3_pH[12,4] 41.520 2.341 33.893 41.950 45.103
beta3_pH[13,4] 33.632 4.888 29.739 31.175 45.173
beta3_pH[14,4] 40.377 4.422 28.929 41.795 45.509
beta3_pH[15,4] 31.447 3.351 28.988 30.094 43.094
beta3_pH[16,4] 31.270 2.864 28.761 29.583 36.429
beta3_pH[11,5] 39.686 1.081 37.450 39.739 42.069
beta3_pH[12,5] 38.302 1.621 35.271 38.258 42.022
beta3_pH[13,5] 39.494 2.828 29.962 40.430 41.466
beta3_pH[14,5] 39.541 1.099 37.769 39.363 42.440
beta3_pH[15,5] 40.143 0.667 38.458 40.292 41.009
beta3_pH[16,5] 38.719 1.427 35.330 38.939 40.763
beta0_pelagic[1] 1.878 0.442 0.703 2.024 2.396
beta0_pelagic[2] 1.344 0.327 0.309 1.434 1.724
beta0_pelagic[3] 0.448 0.262 -0.118 0.455 0.894
beta0_pelagic[4] 0.554 0.327 -0.032 0.550 1.136
beta0_pelagic[5] 0.843 1.127 -2.416 1.294 1.680
beta0_pelagic[6] 1.588 0.155 1.265 1.597 1.857
beta0_pelagic[7] 1.540 0.137 1.271 1.542 1.790
beta0_pelagic[8] 1.857 0.139 1.563 1.861 2.118
beta0_pelagic[9] 2.306 0.497 1.169 2.521 2.886
beta0_pelagic[10] 2.488 0.333 1.535 2.562 2.833
beta0_pelagic[11] 0.671 0.126 0.431 0.673 0.921
beta0_pelagic[12] 1.752 0.134 1.490 1.754 2.018
beta0_pelagic[13] 0.599 0.147 0.299 0.601 0.893
beta0_pelagic[14] 0.385 0.184 0.001 0.394 0.723
beta0_pelagic[15] -0.239 0.131 -0.490 -0.235 0.021
beta0_pelagic[16] 0.538 0.126 0.305 0.536 0.792
beta1_pelagic[1] 0.367 0.447 0.000 0.200 1.559
beta1_pelagic[2] 0.274 0.347 0.000 0.150 1.268
beta1_pelagic[3] 0.584 0.318 0.000 0.607 1.173
beta1_pelagic[4] 0.614 0.368 0.000 0.632 1.262
beta1_pelagic[5] 0.586 1.215 0.000 0.001 4.027
beta1_pelagic[6] 0.092 0.739 0.000 0.000 0.638
beta1_pelagic[7] 12.153 25.332 0.000 0.002 91.890
beta1_pelagic[8] 0.082 0.321 0.000 0.000 0.791
beta1_pelagic[9] 1.087 2.473 0.000 0.056 9.379
beta1_pelagic[10] 0.164 0.456 0.000 0.000 1.423
beta1_pelagic[11] 2.403 0.280 1.906 2.390 3.039
beta1_pelagic[12] 2.627 0.284 2.086 2.621 3.213
beta1_pelagic[13] 2.080 0.425 1.475 2.001 3.277
beta1_pelagic[14] 3.346 0.743 2.207 3.241 5.102
beta1_pelagic[15] 2.534 0.246 2.058 2.537 3.017
beta1_pelagic[16] 3.019 0.262 2.480 3.022 3.530
beta2_pelagic[1] 2.478 5.420 -9.510 2.278 13.692
beta2_pelagic[2] 3.248 5.121 -7.398 2.702 14.937
beta2_pelagic[3] 3.711 3.910 -1.356 2.802 13.187
beta2_pelagic[4] 4.152 4.653 -3.919 3.178 15.692
beta2_pelagic[5] 1.110 7.725 -11.685 -0.617 18.574
beta2_pelagic[6] 0.112 6.396 -12.426 -0.053 13.688
beta2_pelagic[7] -0.758 6.789 -13.560 -1.404 13.649
beta2_pelagic[8] -0.456 6.440 -12.749 -0.858 13.500
beta2_pelagic[9] 0.062 5.573 -8.094 0.387 11.495
beta2_pelagic[10] 0.266 5.934 -12.172 0.608 11.379
beta2_pelagic[11] 5.591 4.029 0.682 4.647 15.790
beta2_pelagic[12] 7.163 3.929 2.253 6.313 17.469
beta2_pelagic[13] 3.014 2.840 0.330 2.464 10.622
beta2_pelagic[14] 0.622 0.924 0.216 0.429 2.442
beta2_pelagic[15] 7.601 4.139 2.227 6.701 18.013
beta2_pelagic[16] 7.270 4.366 1.258 6.367 18.866
beta3_pelagic[1] 28.929 8.570 18.549 25.363 45.506
beta3_pelagic[2] 31.304 9.066 18.398 31.219 45.622
beta3_pelagic[3] 31.425 5.583 23.042 30.431 43.850
beta3_pelagic[4] 28.629 6.273 21.845 26.285 44.786
beta3_pelagic[5] 34.702 9.119 18.816 35.170 45.982
beta3_pelagic[6] 32.223 8.202 18.729 32.373 45.310
beta3_pelagic[7] 28.510 8.752 18.555 26.298 44.940
beta3_pelagic[8] 31.199 7.971 18.833 30.444 45.371
beta3_pelagic[9] 29.483 7.518 18.375 27.743 44.579
beta3_pelagic[10] 30.589 8.520 18.434 30.165 45.173
beta3_pelagic[11] 43.231 0.329 42.542 43.223 43.854
beta3_pelagic[12] 43.464 0.232 43.059 43.460 43.904
beta3_pelagic[13] 42.764 0.896 40.880 42.874 44.578
beta3_pelagic[14] 43.218 1.250 40.793 43.216 45.596
beta3_pelagic[15] 43.265 0.227 42.823 43.244 43.721
beta3_pelagic[16] 43.280 0.334 42.733 43.295 43.746
mu_beta0_pelagic[1] 1.032 0.615 -0.128 1.049 2.123
mu_beta0_pelagic[2] 1.741 0.443 0.608 1.789 2.458
mu_beta0_pelagic[3] 0.618 0.337 -0.075 0.625 1.285
tau_beta0_pelagic[1] 3.968 16.039 0.140 1.594 16.859
tau_beta0_pelagic[2] 5.465 12.787 0.170 2.624 30.059
tau_beta0_pelagic[3] 2.347 1.569 0.390 1.995 6.304
beta0_yellow[1] -0.541 0.191 -0.959 -0.522 -0.219
beta0_yellow[2] 0.485 0.184 0.069 0.502 0.777
beta0_yellow[3] -0.292 0.179 -0.655 -0.280 0.031
beta0_yellow[4] 0.849 0.266 0.130 0.893 1.211
beta0_yellow[5] -1.146 0.420 -1.994 -1.156 -0.307
beta0_yellow[6] 0.248 0.209 -0.167 0.249 0.654
beta0_yellow[7] 0.713 0.734 -1.365 0.983 1.333
beta0_yellow[8] 0.626 0.660 -1.062 0.906 1.272
beta0_yellow[9] -0.026 0.242 -0.494 -0.031 0.462
beta0_yellow[10] 0.238 0.150 -0.058 0.233 0.530
beta0_yellow[11] -1.884 0.524 -2.993 -1.860 -0.896
beta0_yellow[12] -3.448 0.434 -4.350 -3.417 -2.655
beta0_yellow[13] -3.543 0.440 -4.419 -3.528 -2.691
beta0_yellow[14] -2.097 0.542 -3.124 -2.077 -1.077
beta0_yellow[15] -2.743 0.418 -3.675 -2.724 -1.977
beta0_yellow[16] -2.291 0.466 -3.239 -2.285 -1.390
beta1_yellow[1] 0.484 0.446 0.000 0.417 1.589
beta1_yellow[2] 1.060 0.396 0.568 1.011 2.058
beta1_yellow[3] 0.637 0.262 0.075 0.636 1.108
beta1_yellow[4] 1.289 0.620 0.645 1.145 3.222
beta1_yellow[5] 2.852 1.174 1.272 2.730 4.782
beta1_yellow[6] 2.252 0.353 1.538 2.254 2.952
beta1_yellow[7] 4.170 5.790 0.159 2.596 17.864
beta1_yellow[8] 2.197 2.621 0.054 1.629 9.215
beta1_yellow[9] 1.473 0.355 0.811 1.467 2.135
beta1_yellow[10] 2.588 0.463 1.735 2.569 3.576
beta1_yellow[11] 2.034 0.531 1.054 2.013 3.174
beta1_yellow[12] 2.234 0.448 1.446 2.216 3.136
beta1_yellow[13] 2.737 0.443 1.887 2.725 3.642
beta1_yellow[14] 2.153 0.510 1.230 2.113 3.165
beta1_yellow[15] 2.040 0.418 1.303 2.010 2.994
beta1_yellow[16] 2.098 0.464 1.223 2.078 3.045
beta2_yellow[1] -3.942 5.137 -16.704 -3.122 5.501
beta2_yellow[2] -4.757 4.480 -16.665 -3.500 -0.161
beta2_yellow[3] -4.388 3.991 -14.169 -3.328 -0.164
beta2_yellow[4] -5.548 5.520 -18.420 -3.543 -0.110
beta2_yellow[5] -7.340 5.196 -20.351 -6.224 -0.715
beta2_yellow[6] 6.257 4.577 1.129 4.997 18.303
beta2_yellow[7] -5.954 8.225 -19.403 -7.351 11.652
beta2_yellow[8] -2.482 7.714 -17.526 -2.339 13.955
beta2_yellow[9] 6.750 4.682 0.594 5.717 18.096
beta2_yellow[10] -8.051 5.143 -21.059 -7.026 -1.283
beta2_yellow[11] -4.327 2.928 -12.079 -3.557 -1.088
beta2_yellow[12] -4.471 2.861 -12.250 -3.716 -1.206
beta2_yellow[13] -4.447 2.740 -11.553 -3.716 -1.503
beta2_yellow[14] -4.438 3.133 -12.921 -3.669 -0.552
beta2_yellow[15] -4.050 2.652 -11.155 -3.314 -1.064
beta2_yellow[16] -4.675 2.949 -12.448 -3.889 -1.359
beta3_yellow[1] 29.106 8.184 18.382 27.415 45.258
beta3_yellow[2] 29.143 1.636 26.946 28.899 32.672
beta3_yellow[3] 33.283 3.003 27.921 33.067 40.314
beta3_yellow[4] 29.222 3.247 23.922 28.020 36.146
beta3_yellow[5] 33.446 1.351 31.036 33.469 35.521
beta3_yellow[6] 39.603 0.480 38.748 39.572 40.716
beta3_yellow[7] 23.211 5.679 18.476 20.586 42.955
beta3_yellow[8] 25.635 5.027 18.354 25.362 37.602
beta3_yellow[9] 37.833 1.471 36.451 37.619 42.472
beta3_yellow[10] 29.414 0.391 28.436 29.450 29.972
beta3_yellow[11] 45.391 0.510 44.114 45.501 45.980
beta3_yellow[12] 43.365 0.497 42.388 43.324 44.362
beta3_yellow[13] 44.874 0.384 44.008 44.940 45.548
beta3_yellow[14] 44.193 1.705 42.874 44.303 45.886
beta3_yellow[15] 45.286 0.495 44.231 45.325 45.972
beta3_yellow[16] 44.622 0.637 43.455 44.603 45.857
mu_beta0_yellow[1] 0.116 0.458 -0.820 0.113 1.042
mu_beta0_yellow[2] 0.100 0.433 -0.811 0.117 0.923
mu_beta0_yellow[3] -2.449 0.532 -3.326 -2.497 -1.270
tau_beta0_yellow[1] 3.225 9.983 0.179 1.792 10.760
tau_beta0_yellow[2] 2.330 4.285 0.233 1.463 8.976
tau_beta0_yellow[3] 2.884 9.465 0.183 1.419 12.203
beta0_black[1] 0.019 0.196 -0.351 0.016 0.397
beta0_black[2] 1.852 0.197 1.384 1.879 2.122
beta0_black[3] 1.273 0.158 0.914 1.285 1.549
beta0_black[4] 1.977 0.320 1.148 2.002 2.499
beta0_black[5] 1.650 1.347 -1.101 1.669 4.314
beta0_black[6] 1.633 1.418 -1.228 1.643 4.235
beta0_black[7] 1.687 1.468 -0.961 1.696 4.300
beta0_black[8] 1.301 0.219 0.880 1.302 1.712
beta0_black[9] 2.351 0.289 1.664 2.373 2.839
beta0_black[10] 1.469 0.134 1.203 1.472 1.724
beta0_black[11] 3.396 0.249 2.927 3.423 3.737
beta0_black[12] 4.601 0.241 4.163 4.589 5.075
beta0_black[13] 0.236 0.505 -0.462 0.044 1.122
beta0_black[14] 2.198 0.524 0.708 2.289 2.941
beta0_black[15] 1.126 0.311 0.281 1.185 1.530
beta0_black[16] 4.008 0.547 2.347 4.173 4.515
beta2_black[1] 3.014 5.334 -7.696 2.774 14.366
beta2_black[2] -1.240 5.626 -15.110 0.095 9.367
beta2_black[3] 0.267 6.212 -12.854 0.333 14.056
beta2_black[4] -2.759 3.570 -13.436 -1.744 -0.060
beta2_black[5] -0.280 6.225 -13.412 -0.281 13.084
beta2_black[6] -0.092 6.247 -12.788 -0.166 12.861
beta2_black[7] -0.066 6.276 -12.971 -0.075 13.098
beta2_black[8] -0.344 6.232 -13.539 -0.360 12.716
beta2_black[9] -0.413 6.109 -13.132 -0.407 12.895
beta2_black[10] -0.513 4.913 -10.606 -0.409 9.944
beta2_black[11] -2.270 4.701 -13.042 -1.903 7.556
beta2_black[12] -2.909 4.087 -11.487 -2.655 6.285
beta2_black[13] -2.636 4.270 -13.173 -1.999 6.037
beta2_black[14] -2.602 3.730 -12.550 -1.424 1.602
beta2_black[15] -2.584 4.370 -11.720 -2.157 6.865
beta2_black[16] -0.692 4.915 -11.152 -0.224 10.118
beta3_black[1] 38.488 6.640 20.054 41.570 43.883
beta3_black[2] 31.643 8.258 18.599 32.030 45.386
beta3_black[3] 31.495 8.032 18.665 31.235 45.269
beta3_black[4] 33.173 4.059 20.908 33.101 41.722
beta3_black[5] 32.046 8.058 18.839 32.119 45.254
beta3_black[6] 31.980 8.115 18.738 32.060 45.379
beta3_black[7] 31.964 8.052 18.821 31.724 45.449
beta3_black[8] 32.239 8.067 18.745 32.421 45.283
beta3_black[9] 32.280 8.116 18.674 32.632 45.280
beta3_black[10] 31.372 8.157 18.662 30.916 45.310
beta3_black[11] 35.288 5.006 28.373 34.331 45.265
beta3_black[12] 34.274 3.617 29.138 33.112 44.704
beta3_black[13] 38.527 3.238 29.321 39.303 44.419
beta3_black[14] 38.590 3.302 30.331 39.034 45.331
beta3_black[15] 37.341 5.225 28.501 37.419 45.570
beta3_black[16] 35.807 5.436 28.274 35.111 45.524
beta4_black[1] -0.271 0.190 -0.642 -0.271 0.108
beta4_black[2] 0.253 0.175 -0.096 0.252 0.591
beta4_black[3] -0.936 0.182 -1.301 -0.936 -0.583
beta4_black[4] 0.555 0.226 0.126 0.556 1.006
beta4_black[5] 0.209 2.606 -4.681 0.153 5.189
beta4_black[6] 0.172 2.484 -4.451 0.135 5.017
beta4_black[7] 0.217 2.450 -4.762 0.159 5.107
beta4_black[8] -0.722 0.357 -1.427 -0.723 -0.020
beta4_black[9] 1.533 1.037 -0.071 1.397 3.901
beta4_black[10] 0.021 0.182 -0.330 0.021 0.370
beta4_black[11] -0.698 0.209 -1.119 -0.694 -0.293
beta4_black[12] 0.259 0.324 -0.362 0.250 0.909
beta4_black[13] -1.186 0.212 -1.602 -1.180 -0.775
beta4_black[14] -0.133 0.235 -0.592 -0.135 0.340
beta4_black[15] -0.883 0.206 -1.295 -0.883 -0.480
beta4_black[16] -0.592 0.221 -1.042 -0.591 -0.172
mu_beta0_black[1] 1.227 0.688 -0.239 1.241 2.527
mu_beta0_black[2] 1.639 0.659 0.149 1.675 2.806
mu_beta0_black[3] 2.396 0.888 0.576 2.435 4.048
tau_beta0_black[1] 1.273 1.122 0.097 0.974 4.329
tau_beta0_black[2] 4.962 12.781 0.088 2.158 25.628
tau_beta0_black[3] 0.340 0.225 0.055 0.294 0.920
beta0_dsr[11] -3.014 0.275 -3.551 -3.016 -2.462
beta0_dsr[12] 4.476 0.273 3.975 4.470 5.015
beta0_dsr[13] -1.699 0.477 -3.130 -1.626 -1.095
beta0_dsr[14] -4.117 0.487 -5.058 -4.108 -3.175
beta0_dsr[15] -2.404 0.266 -2.923 -2.409 -1.869
beta0_dsr[16] -3.066 0.344 -3.743 -3.059 -2.387
beta1_dsr[11] 4.889 0.290 4.307 4.887 5.446
beta1_dsr[12] 6.050 3.582 2.455 5.191 15.191
beta1_dsr[13] 3.187 0.602 2.514 3.073 5.206
beta1_dsr[14] 6.750 0.514 5.769 6.740 7.770
beta1_dsr[15] 3.592 0.269 3.057 3.595 4.098
beta1_dsr[16] 5.850 0.360 5.145 5.845 6.563
beta2_dsr[11] -10.510 4.458 -21.892 -9.346 -4.872
beta2_dsr[12] -8.393 4.415 -20.249 -7.545 -2.079
beta2_dsr[13] -6.513 4.243 -17.459 -6.007 -0.303
beta2_dsr[14] -6.978 3.444 -15.730 -6.419 -2.345
beta2_dsr[15] -9.535 4.421 -20.685 -8.499 -3.944
beta2_dsr[16] -9.869 4.306 -20.906 -8.794 -4.505
beta3_dsr[11] 43.483 0.163 43.185 43.482 43.793
beta3_dsr[12] 34.024 0.643 32.373 34.149 34.826
beta3_dsr[13] 43.279 0.413 42.761 43.195 44.056
beta3_dsr[14] 43.266 0.154 43.066 43.230 43.648
beta3_dsr[15] 43.471 0.197 43.123 43.466 43.841
beta3_dsr[16] 43.438 0.175 43.144 43.422 43.788
beta4_dsr[11] 0.664 0.211 0.258 0.664 1.075
beta4_dsr[12] 0.321 0.462 -0.586 0.319 1.256
beta4_dsr[13] -0.079 0.209 -0.470 -0.078 0.327
beta4_dsr[14] 0.214 0.250 -0.279 0.218 0.688
beta4_dsr[15] 0.987 0.216 0.574 0.983 1.408
beta4_dsr[16] 0.180 0.229 -0.279 0.180 0.619
beta0_slope[11] -2.004 0.158 -2.307 -2.006 -1.687
beta0_slope[12] -4.655 0.263 -5.184 -4.659 -4.142
beta0_slope[13] -1.459 0.239 -2.065 -1.427 -1.082
beta0_slope[14] -2.677 0.198 -3.047 -2.677 -2.290
beta0_slope[15] -1.698 0.157 -2.000 -1.696 -1.380
beta0_slope[16] -2.761 0.165 -3.083 -2.761 -2.430
beta1_slope[11] 4.376 0.301 3.797 4.378 4.961
beta1_slope[12] 4.827 0.549 3.795 4.828 5.934
beta1_slope[13] 2.781 0.673 1.976 2.629 4.865
beta1_slope[14] 6.133 0.917 4.641 6.020 8.366
beta1_slope[15] 2.018 0.275 1.468 2.013 2.555
beta1_slope[16] 5.290 0.391 4.540 5.281 6.062
beta2_slope[11] 10.599 4.746 4.477 9.489 22.850
beta2_slope[12] 7.901 4.469 1.709 7.030 18.691
beta2_slope[13] 5.578 4.523 0.271 4.759 15.469
beta2_slope[14] 2.278 2.673 0.689 1.319 10.529
beta2_slope[15] 8.763 4.641 2.448 7.721 20.518
beta2_slope[16] 9.763 4.507 3.753 8.734 20.868
beta3_slope[11] 43.492 0.176 43.175 43.492 43.823
beta3_slope[12] 43.370 0.237 42.997 43.340 43.852
beta3_slope[13] 43.600 0.574 42.535 43.620 45.035
beta3_slope[14] 44.646 0.438 43.798 44.645 45.456
beta3_slope[15] 43.597 0.256 43.123 43.602 44.051
beta3_slope[16] 43.462 0.183 43.147 43.449 43.825
beta4_slope[11] -0.458 0.214 -0.882 -0.457 -0.037
beta4_slope[12] -1.249 0.667 -2.744 -1.175 -0.183
beta4_slope[13] 0.184 0.211 -0.225 0.184 0.601
beta4_slope[14] -0.103 0.249 -0.603 -0.101 0.383
beta4_slope[15] -0.204 0.201 -0.600 -0.200 0.186
beta4_slope[16] -0.134 0.224 -0.572 -0.133 0.298
sigma_H[1] 0.196 0.052 0.105 0.194 0.309
sigma_H[2] 0.169 0.030 0.116 0.167 0.236
sigma_H[3] 0.197 0.043 0.124 0.194 0.287
sigma_H[4] 0.426 0.079 0.298 0.419 0.603
sigma_H[5] 0.981 0.209 0.608 0.971 1.410
sigma_H[6] 0.372 0.192 0.034 0.364 0.779
sigma_H[7] 0.303 0.061 0.209 0.294 0.446
sigma_H[8] 0.428 0.098 0.279 0.415 0.642
sigma_H[9] 0.514 0.122 0.327 0.495 0.809
sigma_H[10] 0.217 0.043 0.140 0.214 0.311
sigma_H[11] 0.277 0.045 0.202 0.274 0.381
sigma_H[12] 0.449 0.165 0.216 0.426 0.779
sigma_H[13] 0.216 0.037 0.150 0.213 0.300
sigma_H[14] 0.505 0.094 0.343 0.500 0.711
sigma_H[15] 0.249 0.041 0.181 0.246 0.341
sigma_H[16] 0.231 0.044 0.158 0.227 0.328
lambda_H[1] 3.058 4.099 0.144 1.786 13.804
lambda_H[2] 8.052 7.368 0.820 5.896 28.361
lambda_H[3] 6.256 9.841 0.266 3.095 31.641
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.516 9.243 0.027 0.799 26.556
lambda_H[6] 7.524 14.609 0.008 0.915 50.676
lambda_H[7] 0.014 0.010 0.002 0.011 0.041
lambda_H[8] 8.089 10.665 0.047 4.328 38.565
lambda_H[9] 0.016 0.010 0.003 0.013 0.043
lambda_H[10] 0.292 0.440 0.033 0.191 1.043
lambda_H[11] 0.246 0.358 0.013 0.129 1.102
lambda_H[12] 4.891 6.128 0.185 2.912 21.325
lambda_H[13] 3.300 3.017 0.256 2.421 11.172
lambda_H[14] 3.723 4.650 0.276 2.248 15.761
lambda_H[15] 0.028 0.076 0.003 0.017 0.111
lambda_H[16] 1.713 2.235 0.085 0.981 7.673
mu_lambda_H[1] 4.337 1.888 1.285 4.151 8.426
mu_lambda_H[2] 3.824 1.975 0.624 3.667 8.094
mu_lambda_H[3] 3.596 1.870 0.809 3.307 7.784
sigma_lambda_H[1] 8.616 4.296 2.064 7.986 18.258
sigma_lambda_H[2] 8.290 4.651 0.989 7.704 18.509
sigma_lambda_H[3] 6.302 3.921 1.037 5.459 15.890
beta_H[1,1] 6.917 1.066 4.418 7.081 8.489
beta_H[2,1] 9.870 0.487 8.808 9.898 10.751
beta_H[3,1] 7.985 0.772 6.155 8.059 9.252
beta_H[4,1] 9.339 7.951 -7.079 9.523 24.582
beta_H[5,1] -0.053 2.519 -5.552 0.130 4.354
beta_H[6,1] 3.301 3.996 -6.675 4.671 7.849
beta_H[7,1] 1.003 5.689 -10.927 1.486 11.202
beta_H[8,1] 1.557 4.845 -2.458 1.219 3.849
beta_H[9,1] 13.208 5.735 2.261 13.136 24.907
beta_H[10,1] 7.100 1.721 3.477 7.146 10.462
beta_H[11,1] 5.228 3.381 -2.539 5.854 9.975
beta_H[12,1] 2.599 1.027 0.765 2.556 4.750
beta_H[13,1] 9.059 0.936 7.092 9.128 10.561
beta_H[14,1] 2.189 1.008 0.258 2.171 4.283
beta_H[15,1] -5.919 3.959 -12.965 -6.198 2.597
beta_H[16,1] 3.062 2.006 -0.629 2.947 7.335
beta_H[1,2] 7.908 0.244 7.418 7.916 8.369
beta_H[2,2] 10.023 0.140 9.739 10.028 10.299
beta_H[3,2] 8.952 0.197 8.565 8.950 9.331
beta_H[4,2] 3.592 1.488 0.802 3.536 6.735
beta_H[5,2] 1.976 0.977 0.052 1.976 3.815
beta_H[6,2] 5.789 1.105 3.298 5.997 7.478
beta_H[7,2] 2.494 1.100 0.590 2.376 4.925
beta_H[8,2] 2.916 1.318 1.056 3.113 4.205
beta_H[9,2] 3.406 1.087 1.328 3.405 5.598
beta_H[10,2] 8.177 0.354 7.458 8.186 8.829
beta_H[11,2] 9.720 0.609 8.801 9.612 11.143
beta_H[12,2] 3.935 0.366 3.254 3.918 4.676
beta_H[13,2] 9.115 0.257 8.652 9.105 9.644
beta_H[14,2] 4.008 0.347 3.323 4.006 4.710
beta_H[15,2] 11.336 0.709 9.850 11.381 12.617
beta_H[16,2] 4.700 0.789 3.188 4.703 6.203
beta_H[1,3] 8.489 0.246 8.043 8.474 9.010
beta_H[2,3] 10.070 0.117 9.844 10.070 10.303
beta_H[3,3] 9.623 0.164 9.305 9.620 9.954
beta_H[4,3] -2.578 0.882 -4.369 -2.538 -0.909
beta_H[5,3] 3.986 0.631 2.692 3.997 5.151
beta_H[6,3] 8.136 1.194 6.509 7.780 10.718
beta_H[7,3] -2.605 0.747 -4.081 -2.616 -1.212
beta_H[8,3] 5.280 0.618 4.639 5.188 6.617
beta_H[9,3] -2.665 0.738 -4.155 -2.652 -1.271
beta_H[10,3] 8.732 0.275 8.205 8.723 9.288
beta_H[11,3] 8.536 0.279 7.934 8.556 9.029
beta_H[12,3] 5.239 0.326 4.479 5.285 5.768
beta_H[13,3] 8.824 0.183 8.455 8.830 9.164
beta_H[14,3] 5.700 0.268 5.130 5.721 6.179
beta_H[15,3] 10.368 0.332 9.711 10.368 11.027
beta_H[16,3] 6.684 0.539 5.427 6.759 7.549
beta_H[1,4] 8.279 0.173 7.914 8.290 8.593
beta_H[2,4] 10.128 0.121 9.875 10.135 10.343
beta_H[3,4] 10.113 0.166 9.751 10.129 10.400
beta_H[4,4] 11.793 0.443 10.933 11.799 12.647
beta_H[5,4] 5.704 0.806 4.372 5.616 7.552
beta_H[6,4] 7.187 0.897 5.136 7.456 8.424
beta_H[7,4] 8.216 0.358 7.531 8.211 8.936
beta_H[8,4] 6.691 0.290 6.126 6.713 7.135
beta_H[9,4] 7.183 0.470 6.277 7.184 8.114
beta_H[10,4] 7.743 0.240 7.285 7.735 8.259
beta_H[11,4] 9.292 0.206 8.890 9.285 9.700
beta_H[12,4] 7.124 0.217 6.725 7.119 7.581
beta_H[13,4] 9.013 0.145 8.723 9.016 9.289
beta_H[14,4] 7.670 0.213 7.235 7.667 8.105
beta_H[15,4] 9.442 0.244 8.953 9.444 9.926
beta_H[16,4] 9.155 0.207 8.795 9.139 9.605
beta_H[1,5] 8.985 0.142 8.690 8.985 9.263
beta_H[2,5] 10.779 0.092 10.601 10.776 10.971
beta_H[3,5] 10.920 0.177 10.600 10.912 11.290
beta_H[4,5] 8.387 0.470 7.478 8.373 9.317
beta_H[5,5] 5.394 0.625 3.954 5.471 6.434
beta_H[6,5] 8.746 0.566 7.914 8.629 10.108
beta_H[7,5] 6.780 0.338 6.113 6.777 7.455
beta_H[8,5] 8.222 0.245 7.847 8.200 8.698
beta_H[9,5] 8.208 0.483 7.209 8.208 9.161
beta_H[10,5] 10.092 0.226 9.634 10.093 10.534
beta_H[11,5] 11.537 0.233 11.069 11.533 11.989
beta_H[12,5] 8.466 0.206 8.063 8.459 8.885
beta_H[13,5] 10.020 0.130 9.771 10.020 10.272
beta_H[14,5] 9.188 0.229 8.764 9.172 9.645
beta_H[15,5] 11.172 0.247 10.699 11.174 11.647
beta_H[16,5] 9.942 0.156 9.624 9.949 10.235
beta_H[1,6] 10.182 0.192 9.859 10.162 10.606
beta_H[2,6] 11.512 0.108 11.309 11.512 11.723
beta_H[3,6] 10.803 0.164 10.440 10.815 11.095
beta_H[4,6] 12.875 0.827 11.200 12.897 14.437
beta_H[5,6] 5.922 0.605 4.749 5.904 7.125
beta_H[6,6] 8.812 0.615 7.214 8.911 9.726
beta_H[7,6] 9.820 0.563 8.753 9.819 10.934
beta_H[8,6] 9.513 0.324 8.892 9.543 9.983
beta_H[9,6] 8.456 0.790 6.951 8.449 9.995
beta_H[10,6] 9.503 0.320 8.842 9.531 10.048
beta_H[11,6] 10.796 0.363 10.004 10.820 11.470
beta_H[12,6] 9.378 0.258 8.891 9.369 9.924
beta_H[13,6] 11.060 0.166 10.771 11.053 11.401
beta_H[14,6] 9.878 0.290 9.287 9.881 10.421
beta_H[15,6] 10.868 0.430 10.011 10.864 11.710
beta_H[16,6] 10.565 0.208 10.125 10.574 10.945
beta_H[1,7] 10.874 0.880 8.727 10.988 12.293
beta_H[2,7] 12.209 0.426 11.367 12.211 13.078
beta_H[3,7] 10.542 0.678 9.053 10.603 11.689
beta_H[4,7] 2.484 4.253 -5.759 2.417 11.103
beta_H[5,7] 6.553 1.982 3.107 6.440 11.158
beta_H[6,7] 9.415 2.365 4.555 9.415 15.224
beta_H[7,7] 10.680 2.790 5.242 10.703 16.133
beta_H[8,7] 11.013 1.197 9.347 10.937 13.049
beta_H[9,7] 4.468 4.030 -3.515 4.502 12.438
beta_H[10,7] 9.873 1.463 7.171 9.775 13.065
beta_H[11,7] 11.068 1.787 7.693 10.921 14.922
beta_H[12,7] 9.995 0.985 7.805 10.100 11.564
beta_H[13,7] 11.664 0.794 9.892 11.759 12.873
beta_H[14,7] 10.519 0.927 8.465 10.577 12.181
beta_H[15,7] 12.105 2.278 7.703 12.095 16.708
beta_H[16,7] 11.914 1.029 10.288 11.778 14.486
beta0_H[1] 8.848 13.295 -18.737 8.878 36.958
beta0_H[2] 10.475 6.480 -3.077 10.561 23.253
beta0_H[3] 9.906 9.987 -10.285 9.810 29.974
beta0_H[4] 3.840 184.205 -374.843 3.466 368.873
beta0_H[5] 3.740 27.582 -51.640 4.272 57.592
beta0_H[6] 8.677 49.946 -96.591 7.887 121.951
beta0_H[7] 6.841 131.895 -252.891 4.053 268.617
beta0_H[8] 6.651 38.016 -18.796 6.456 32.363
beta0_H[9] 6.767 118.916 -238.160 6.686 247.510
beta0_H[10] 9.400 33.438 -54.587 8.808 78.846
beta0_H[11] 10.018 47.424 -84.411 9.562 113.381
beta0_H[12] 6.850 11.376 -13.586 6.658 28.256
beta0_H[13] 10.252 11.530 -10.964 10.144 31.566
beta0_H[14] 7.499 11.709 -14.144 7.330 31.849
beta0_H[15] 10.688 108.941 -198.753 9.895 231.617
beta0_H[16] 8.360 18.310 -28.227 8.228 47.240